ZSquared NecklaceThe signature piece for Tom Banchoff's 1996 artshow, Surfaces Beyond the Third Dimension, this image shows five views of the graph of the complex squaring function, each from a different viewpoint in complex 2space (or real 4space). They are part of a sequence formed by rotating the graph in four dimensions (or equivalently, walking around the graph). The rotation is chosen so that, as a projection into a plane, the image has threefold rotational symmetry (the boundary curves form epi and hypocycloids of a circle). Movies and a more complete discussion of the mathematics behind this image are available at the virtual art exhibit. This surface is also the subject of ZSquared Tetraview.


